A rose by any other name

Publication date:
May 20, 2013 9:15:42 PM

The picture represents a "finite energy foliation"
of the 3-dimensional manifold S1 x S2 with its standard contact structure. Finite energy
foliations are ways of filling 3-dimensional space with smooth surfaces that
are solutions to a differential equation arising in string theory.

Such pictures can help mathematicians gain
insight into problems in dynamical systems and in topology – for example, an
important strand in research by Chris Wendl (UCL Mathematics) has been using finite
energy foliations to try and answer the question, “how many different 4-dimensional
shapes could this 3-dimensional shape be the boundary of?

One can use this particular picture to deduce
that the answer is exactly one.

Credit: Chris Wendl (UCL Mathematics)

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